The present invention generally relates to smoothing methods and apparatuses, and more particularly to a smoothing method and a smoothing apparatus for smoothing a contour of a dot pattern of a character which is enlarged and reduced. The present invention is suited for application in a desk top publishing system, a personal computer, a word processing system, a digital facsimile machine and the like wherein a basic character font constituted by a dot pattern is enlarged or reduced when outputted.
When reading out from a font memory a basic character font which is constituted by a dot pattern, there is often a need to enlarge or reduce the size of the basic character font. When enlarging the basic character font, each black (or white) dot of the basic character font is converted into a group of black (or white) dots of a number dependent on the magnification. For example, when enlarging a 24.times.24 dot pattern of a character (hereinafter referred to as a dot character pattern) with a magnification of 2 into a 48.times.48 dot character pattern, one dot is converted into a matrix arrangement of 2.times.2 (=4) dots. Similarly, when reducing the 24.times.24 dot character pattern with a magnification of 2/3 into a 16.times.16 dot character pattern, a matrix arrangement of 3.times.3 (=9) dots is converted into a matrix arrangement of 2.times.2 (=4) dots. However, when the dot character pattern is enlarged and reduced in the above described manner, the contour of the character includes gathers and is extremely deformed from the contour of the original character. As a result, the enlarged or reduced character lacks smoothness in the contour thereof, and the shape and form of the character is deformed.
As one method of preventing the unwanted deformation of the character when the character is enlarged, there is a method disclosed in a Japanese Published Patent Application No. 53-24146 which makes an interpolation at a stepped corner portion of a group of dots having a matrix arrangement by adding a group of dots which are arranged in a right-angled isosceles triangular shape of an appropriate size so as to smoothen the contour of the enlarged dot character pattern. However, according to this method, an oblique line having an inclination other than 45 degrees does not become a rectilinear line after the enlargement and interpolation. For example, when an oblique line having an inclination of 3/5 is enlarged and subjected to the interpolation referred above, the oblique line after the enlargement and interpolation includes gathers and does not become a rectilinear line.
In order to prevent the oblique line from becoming gathered after the enlargement and interpolation, it is possible to conceive a method of fitting to the oblique line portion a rectilinear line which is as long as possible for the interpolation. But in this case, curves which have a large curvature all become rectilinear lines after the interpolation and there is a problem in that it is impossible to describe delicate curves of the character.
As an alternative methods, there are smoothing methods which use a spline curve or a Bezier curve, but these methods require complex processes and an extremely long time to carry out such complex processes. Furthermore, there is also a problem in that a digital coordinate representation is unsuited in the case of quadratic curves or curves of higher order.